SOLUTION

As we know that

• N ∝ Eb / Φ

This equation tells us that the speed of the motor (N) is directly proportional to the back EMF (Eb) and inversely proportional to the flux (Φ).

• N ∝ (V – IRa) / Φ

This equation is a modification of the first equation, where:

• V is the supply voltage
• I is the armature current
• Ra is the armature resistance

The speed of a DC motor can be controlled by varying several parameters. The correct options for controlling the speed of a DC motor are

1. Applied Voltage: The speed of a DC motor is directly proportional to the voltage applied across the armature. By increasing or decreasing this voltage, the speed of the motor can be controlled. By controlling the armature voltage below the rated value, the speed can be controlled only below the rated value.
   • Because the voltage can’t be above the rated value due to the insulation failure of winding.
   • This method is used for the separately excited motor but not suitable for the shunt motor because flux will change due to a change in voltage.
2. Flux per Pole: The speed is inversely proportional to the magnetic flux per pole. By varying the field current (which changes the flux), you can control the speed of the motor. Reducing the flux increases the speed, while increasing the flux decreases it.
3. Resistance of Armature Circuit: Introducing resistance in series with the armature reduces the current flowing through it, which in turn affects the back EMF and thus alters the speed of the motor. Increasing armature resistance will decrease speed, while decreasing resistance will increase speed.
   • Increasing the resistance of the armature circuit (Ra) will decrease the motor current (I) and consequently reduce the speed
   • This method gives only below base speeds.
   • In this method, the motor acts as constant torque and a variable power drive.